There appears to be a fundamental misunderstanding that is not being addressed. Please forgive me if I am wrong, but the original question suggests that the writer is not familiar with the distinction between 32-bit and 64-bit hardware systems.
Here is a link to a good summaryFundamentally, 32-bit and 64-bit refer to the 'width' of the data that can be handled by a computer. The first IBM-PC was, I think, an 8-bit system. This limited the amount of memory the system could use at one time, the amount of data that could be processed at a time, and maybe the number of tasks that could be handled in a given clock cycle.
OK, I'm probably wrong in the details, but it's a lot like that.The DOS operating system was designed to work on an 8-bit system, and so was an 8-bit OS. I think later versions would work in a 16-bit system.
The 80386 processor from Intel could address 32-bits, but (and this is why I bring it up) many motherboards still existed that worked with 16-bit bandwidth. Intel made another processor called the 80386sx, which did its internal calculations in a 32-bit address, but interacted with the rest of the PC using 16-bits. The CPU chip was 32-bit, while the motherboard was 16-bit. So, on the
hardware side, if you had a full 80386 CPU and 32 bit motherboard, your system was considered a 32-bit system.
Except that you were probably running Windows 3.1 or something. This is the software side of the system. The operating system, Windows 3.1, was a 16-bit OS. It would not necessarily use all of the features of the 32-bit hardware system. It wasn't until Windows 95 came out that you would have a fully 32-bit PC.
*Disclaimer: I am making this up from my fuzzy memory of days long past. I may be wrong, but I am fundamentally correct, I think.*All right. So we're looking at Zorin-OS, which has 32-bit and 64-bit versions. If your hardware is built to address 64-bit data, then you could download and install 64-bit Zorin-OS. If your hardware is built to address 32-bit data, then the 64-bit Zorin-OS will not work. On the other hand, if your hardware is built for 64-bit operations, it can support
either the 32-bit or 64-bit versions of Zorin-OS.
Since the hardware capability of 64-bit vs 32-bit is built-in, there is no way to change your CPU from 32-bit to 64-bit. You can only replace the 32-bit processor with a 64-bit processor. However, if your hardware motherboard and other components do not themselves work with a 64-bit CPU, there is no point, or maybe it cannot be done at all.
That all being said, I'd stick with the 32-bit Zorin-OS for best compatibility.